Solve the 5 problems using Microsoft Excel Program or SPSS or manually (pen and Paper)

1 Assignment 4 (Sampling Methods and the Central Limit Theorem ) DSRT734 Fall 2020 Assignment due on Sunday Oct 4. 1. The American Auto Association reports that the mean price per gallon of regular gasoline is $3.10, with a population standard deviation of $0.20. Assume a random sample of 16 gasoline stations is selected and their mean cost for regular gasoline is computed. What is the probability that the sample mean is between $2.98 and $3.12? 2. The American Auto Association reports that the mean price per gallon of regular gasoline is $3.10, with a population standard deviation of $0.20. Assume a random sample of 16 gasoline stations is selected and their mean cost for regular gasoline is computed. What is the probability that the difference between the sample mean and the population mean is less than 0.01? 2 3.. The American Auto Association reports that the mean price per gallon of regular gasoline is $3.10, with a population standard deviation of $0.20. Assume a random sample of 16 gasoline stations is selected and their mean cost for regular gasoline is computed. What is the likelihood the sample mean is greater than $3.08? 4. LongLast Inc. produces car batteries. The mean life of these batteries is 60 months. The distribution of the battery life closely follows the normal probability distribution with a standard deviation of eigh t months. As part of its testing program, LongLast tests a sample of 25 batteries. What is the standard error of the mean? 5.. LongLast Inc. produces car batteries. The mean life of these batteries is 60 months. The distribution of the battery life closely follows the normal probability distribution with a standard deviation of eight months. As a part of its testing program, LongLast tests a sample of 25 batteries. What p roportion of the samples will have a mean useful life of more than 56 months?